The Hausdorff Moment Problem under Finite Additivity

Enrique Miranda (), Gert Cooman () and Erik Quaeghebeur ()
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Enrique Miranda: Rey Juan Carlos University
Gert Cooman: Ghent University, Systems Research Group
Erik Quaeghebeur: Ghent University, Systems Research Group

Journal of Theoretical Probability, 2007, vol. 20, issue 3, 663-693

Abstract: We investigate to what extent finitely additive probability measures on the unit interval are determined by their moment sequence. We do this by studying the lower envelope of all finitely additive probability measures with a given moment sequence. Our investigation leads to several elegant expressions for this lower envelope, and it allows us to conclude that the information provided by the moments is equivalent to the one given by the associated lower and upper distribution functions.

Keywords: Hausdorff moment problem; coherent lower prevision; lower distribution function; complete monotonicity (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1007/s10959-007-0055-4

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